Channel Allocation in a Communication System

ABSTRACT

Methods and systems are described which provide solutions for determining how to allocate terminals to slots in order to maximise communication system performance in the case where there is no feedback channel between a multiuser satellite receiver and terminals within the field of view. Terminals operate independently of each other and choose transmission slots based upon the geographic position of the terminal. Terminals can be programmed with a slot selector to choose slots according to some deterministic or non deterministic function of the current position. A slot plan database may be used to assist in efficient slot selection. Regular and irregular grid based allocation methods are described, that reduce the likelihood that too many terminals transmit using the same slot within the field of view. Satellite induced Doppler effects can be utilised be further increase slot re-use and to improve allocation of slots so that the receiver sees an approximately uniform distribution of frequencies over the frequency band to improve system throughput. The approaches described herein greatly reduce or eliminate the probability of failure at the receiver, which has numerous implementation advantages such as reduced cost, complexity, and power consumption.

PRIORITY DOCUMENTS

The present application claims priority from Australian ProvisionalPatent Application No. 2012903489 titled “Channel allocation in acommunication system” filed on 14 Aug. 2012; the content of which ishereby incorporated by reference in its entirety.

INCORPORATION BY REFERENCE

The following co-pending patent applications are referred to in thefollowing description:

Australian Provisional Patent Application No. 2012904130 titled“Communication system and method” filed on 21 Sep. 2012; and

Australian Provisional Patent Application No. 2012904145 titled“Multiaccess Communication System” filed on 21 Sep. 2012.

The content of each of these applications is hereby incorporated byreference in their entirety.

TECHNICAL FIELD

The present invention relates to wireless communication systems. In aparticular form the present invention relates to allocation of terminalsto slots in wireless communication systems lacking feedback channels.

BACKGROUND

FIG. 1A shows a wireless communication system 1 in which a receiver 2,labelled RX wishes to receive data from each of k user terminals 10(henceforth referred to as terminals), labelled TX₁, TX₂, . . . ,TX_(k), in its field of view 3 (there could also be multiple receiversand multiple corresponding fields of view). Communications takes placeover a medium 5 which must be shared among all the terminals. Theterminals may be stationary (at a fixed location), or they may be mobilee.g. portable, or fitted to a vehicle, aircraft or vessel, or spacevehicle, or carried by a person or animal). We are interested in thecase where there is no feedback channel from the receiver to thetransmitters.

The absence of a feedback channel may be desirable to reduce theimplementation complexity, cost, or power consumption of a terminal,since the terminal does not need to provide communications receiverfunctionality. This is of particular importance in situations, such asfield deployable sensors, where terminals may be battery powered, orhave a limited power source. Systems with no feedback channel from thereceiver to the terminals will be called “open-loop”.

There are several examples of systems which fit this model. These aredescribed for illustrative purposes only, and are not intended torestrict the application of the described methods.

One example is a low earth orbit satellite communications, where thefield of view is the footprint of the satellite, and the transmittersare ground based sensor devices equipped with wireless transmitters forthe purposes of transmitting sensor data to the satellite. In thisexample, the field of view moves over the surface of the earth as thesatellite orbits. From an orbital altitude of 700 km, the field of viewis of the order of 6000 km wide. FIG. 1B shows an example of acommunication system with a satellite receiver with a moving field ofview for communicating with k transmitters. At a first point in time thereceiver has a first field of view 6 which contains transmitters TX₁,and TX₂. At a later time, the satellite has moved to the right, and thushas a new field of view 7 which contains transmitters TX_(i), TX_(j) andTX_(k). In one scenario, power consumption is critical for both theground based sensors and the satellite payload. In order to increase thelifetime of the sensors and to reduce the cost of the payload it may beadvantageous to have no feedback link from the satellite to the sensors.

Another example is cellular communications, where the field of view isthe coverage area (sometimes called a cell) of a particular basestation. Again, the terminals may be low cost sensors equipped withcellular transmitters in order to send their sensor data to the basestation but lacking a feedback channel to allow coordination oftransmissions as is typically performed in cellular communicationssystems.

The shared physical communications medium may be partitioned into anumber of channels. These channels may be time slots in a time divisionmultiple access system, frequency slots in a frequency division multipleaccess system, subcarriers in an orthogonal frequency division multipleaccess system, or spreading sequences in a code division multiple accesssystem. More generally, the slots may be hybrids of any of these, wherea slot corresponds to some subset of the overall degrees of freedom ofthe system (including degrees of freedom resulting from the use ofmultiple transmit and or receive antennas). Regardless of the underlyingmethod of dividing the medium into channels, we shall refer to thesechannels as “slots”. We do not require that the slots be orthogonal,although in many instances slots are chosen to be orthogonal.

In some embodiments the receiver is equipped with a multiuser decoderthat is capable of successfully decoding some number of simultaneoustransmissions by different terminals within the same slot. In practice,the number of simultaneous transmissions within a slot that can besuccessfully decoded depends on a variety of systems parameters,including the received signal to noise ratio, the radio channelpropagation characteristics between each terminal and the receiver, andthe kind of multiuser decoder being used. For the sake of a simpleexplanation, we will assume that the multiuser receiver can successfullydecode m≧1 simultaneous transmissions within a single slot. Moredetailed receiver characteristics can be easily taken into account ifthey are known.

However in such systems a problem exists in determining how to allocateterminals to slots in order to maximise system performance. There areseveral metrics of system performance that could be adopted. We areinterested in improving the probability that the receiver can correctlydecode the data transmitted by the terminals. In other words, we wouldlike to minimise the probability that the number of simultaneoustransmissions exceeds m in a given slot, where m is the receivercharacteristic described above (ie the maximum number of transmissionsin a slot that the receiver can successfully decode).

The allocation of terminals to slots is made more difficult by the lackof a feedback channel from the receiver. This prevents the use ofcoordinated slot allocation in which the allocation is performed by somecentral controller. There are a number of known approaches to thisproblem such as fixed allocation, and random access.

A fixed allocation method permanently allocates one slot to eachterminal. This is an instance of circuit switching where the slot isallocated for the entire duration of system operation. This approach hasseveral well-known disadvantages. It is wasteful of channel resources,as it does not allow slots to be re-used. Furthermore, the slotallocations must be hard-wired into the terminals when the system isopen-loop, as there is no other way to control the channel allocationafter deployment. In a system where the terminals are mobile (or wherethe field of view itself moves, for example in a low-earth-orbitsatellite system), it may not be known in advance which terminals willbe in the field of view. As a result, fixed allocation can assign onlyup to m terminals to any one slot. In a satellite communicationscontext, this slot would not be able to be reused by any other terminalsglobally.

Another well-known approach to slot allocation is random access (alsoknown as slotted ALOHA). In this approach, slots are assigned toterminals randomly. Suppose that we have k terminals in the field ofview and n available slots. Under the random access approach, eachterminal selects a slot uniformly at random. Then the probability that aparticular slot is chosen by m terminals is

$\begin{matrix}{P_{m} = {\begin{pmatrix}k \\m\end{pmatrix}\begin{pmatrix}1 \\n\end{pmatrix}^{m}\begin{pmatrix}{n - 1} \\n\end{pmatrix}^{k - m}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

This is known to be well approximated by the Poisson approximation tothe binomial distribution:

$\begin{matrix}{{P_{m} \approx {\frac{1}{m!}^{- \lambda}\lambda^{m}\mspace{14mu} {where}\mspace{14mu} \lambda}} = \frac{k}{n}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

Using this approximation, the probability that a slot has more than mterminals is 1−Q(m+1, λ) where

$\begin{matrix}{{Q\left( {a,z} \right)} = {\frac{\Gamma \left( {a,z} \right)}{\Gamma (a)} = {\frac{1}{\left( {a - 1} \right)!}{\int_{z}^{\infty}{t^{a - 1}^{- t}{t}}}}}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

is the regularised incomplete gamma function. FIG. 2 plots curves 20 ofthe probability that a slot has more than m terminals versus λ=k/n form=1, 2, . . . , 10. Given a particular target decoder failureprobability p, which is the probability that a slot contains more than mterminals, we can compute the maximum value of λ=k/n that is supportedfor this random access scheme as:

λ(p)=Q ⁻(m+1,1−p)   Equation 4

where Q⁻¹ is the inverse regularised gamma function (which can be easilynumerically computed using software such as Mathematica). Curves 30 ofthe maximal values of λ(p) versus m for p=10⁻¹, 10⁻², . . . , 10⁻⁶ areplotted in FIG. 3. From this figure, we see that if we desire a very lowprobability of decoder failure, we are restricted to a low value ofλ=k/n. For example at p=10⁻⁶ and m=5, we can only support k≈n/3terminals in n slots, despite being able to decode 5 simultaneous usersin a slot. If we are willing to accept a higher probability of decoderfailure, then we can support many more terminals. For example, at p=0.1and m=5, we can support k=3n terminals. However in cases where there isno feedback channel, a higher probability is typically less desirable,as there is no way to request retransmission of failed transmissions.

There is thus a need to provide methods and systems for determining howto allocate terminals to slots in order to improve, and if possible,maximise system performance compared to such fixed and random accessallocation schemes, or alternatively to at least provide users with auseful alternative to such schemes.

SUMMARY

According to a first aspect, there is provided a method for allocating atransmission slot to a terminal in a communication system, thecommunication system comprising a plurality of terminals and a commonreceiver for receiving transmissions from the plurality of terminals,the common receiver having a field of view, the method comprising:

obtaining the current geographic position of the terminal; and

allocating a transmission slot based upon the obtained geographicposition of the terminal.

According to a second aspect, there is provided terminal for use in acommunication system comprising:

a transmitter;

a position module which obtains a position of the terminal; and

a slot selector module for selecting a transmission slot based upon theobtained position.

In further aspects of the method and terminal, the current (geographic)position may be a stored position, an estimated position (eg from GPSsignals) or received over a wired or wireless communication link. Theobtained position may be an estimate or approximation of the actualposition. The position may be obtained from a position determinationmodule. The position determination module may provide position updates(periodically, continuously, or on request). In a further aspect thereis no feedback channel from the common receiver to the plurality ofterminals or a feedback channel from the common receiver to theplurality of terminals is present but is not being used for allocationof a transmission slot and allocation of a transmission slot to theterminal is performed independently of the common receiver or otherterminals.

In a further aspect, the slot selection (or allocation) uses a slot plandatabase that comprises a plurality of geographic regions, and eachgeographic region is associated with a set of one or more slots.Allocation is performed by determining the geographic region thatcontains the geographic position of the terminal and selecting a slotfrom the set of one or more slots associated with the determinedgeographic region. The slot plan used by the slot plan database mayallocate each slot one or more times within the field of view. In afurther aspect each slot is allocated at most a fixed number of timeswithin the field of view. The use of geographic information allowsspatial re-use, in which the same slots used in the field of view arere-used elsewhere in a non-overlapping field of view. The regions may bestored as rectangular regions which form a rectangular grid. This gridcan be used to tile the plane to allow reuse of slots. In one aspect theboundaries of the regions are irregular such that regions form anirregular partition of an operational region defined by the plurality ofgeographic regions. Allocation may be performed using a graph-colouringalgorithm. Graph colouring may be used for cases for cases where theboundaries of the region are regular (eg form a rectangular grid), aswell as for cases where the boundaries of the region are irregular. Inone aspect each region is associated with a single vertex in a graph,and an edge is created between any pair of vertexes in the graph whichare within a bounding region. This may be a circle with diameter D, andmay be the smallest circle that completely bounds the estimated field ofview of the common receiver. In one aspect each of the geographicregions is a rectangle geographic region and the slot database stores NMgeographic regions which form a rectangular grid with sides of length Xand Y, where N is the number of columns in the grid and M is the numberof rows in the grid the rectangular grid, and the step of determiningthe geographic region that contains the geographic position (x,y) of theterminal comprises determining the geographic region number R usingR=N(y mod Y)+(x mod X). In one aspect the dimensions (X, Y) of therectangular grid are determined based upon the estimated field of viewof the common receiver (for example the rectangular grid may bound thefield of view). Further reuse can be achieved by taking into accountDoppler effects, for example to split the grid into positive andnegative Doppler regions so that slots may be reused in the two regions.Consider the case of the rectangular grid, X=2Y where the Y dimension isaligned with the direction of motion of the common receiver and thedimensions (X, Y) of the rectangular grid approximately bound half ofthe field of view of the common receiver. In one aspect the step ofassigning a set of one or more slots to each geographic region includesan assignment wherein the same set of slots are used for both a firstregion and a second region, and the first and second regions correspondto different regions in a common field of view of the common receiver,the first region having positive Doppler offsets and the second regionhaving negative Doppler offsets. Allocation of slots may be performed sothat the receiver sees an approximately uniform distribution offrequencies over the frequency band. This may be further based uponobtaining a probability density function q* for the transmissionfrequencies used by the terminals. The probability density function q*for the transmission frequencies used by the terminals may itself beuniform. In one aspect the probability density function q* for thetransmission frequencies used by the terminals is limited to be within apredefined bandwidth, for example based upon system or regulatoryconstraints. The probability density function q* may be obtained basedupon numerical optimisation techniques. In a further aspect, geographicallocation may be used to obtain a set of slots for a local group oftransmitters, and selection of a slot in the set of slots by a terminalis locally coordinated with the local group of terminals.

In a further aspect a communication system is provided comprising aplurality of terminals according to the second aspect (and furtheraspects) and a common receiver for receiving transmissions from theplurality of terminals. In a further aspect a receiver for use in thecommunication system may be provided.

BRIEF DESCRIPTION OF DRAWINGS

Various embodiments will be discussed with reference to the accompanyingdrawings wherein:

FIG. 1A is a schematic diagram of a communications system comprising ofk transmitters communicating with a receiver according to an embodiment;

FIG. 1B is a schematic diagram of a communications system comprising asatellite receiver with a moving field of view for communicating with ktransmitters according to an embodiment;

FIG. 2 is plot of the probability of decoder failure versus λ=k/n form=1, 2, . . . , 10;

FIG. 3 is a plot of the maximum λ(p) versus m for p=10⁻¹, 10⁻², . . . ,10⁻⁶;

FIG. 4 is a block diagram of a terminal with geographic location basedslot selection according to an embodiment;

FIG. 5 is a schematic diagram of a grid based slot allocation schemeaccording to an embodiment;

FIG. 6 is a schematic diagram illustrating tiling of a plane using arectangular grid according to an embodiment;

FIG. 7 is a schematic diagram of the irregular partitioning of an areaaccording to an embodiment;

FIG. 8 is a schematic diagram of irregular grid slot allocation schemeaccording to an embodiment;

FIG. 9 is a schematic diagram of a slot plan database stored as a treeaccording to an embodiment;

FIG. 10 is a schematic diagram of a communications system using of localcoordination of transmitters according to an embodiment;

FIG. 11 is a block diagram of a terminal with local slot coordinationaccording to an embodiment;

FIG. 12 is plot of the Doppler offset of terminals in the field of viewof a low earth orbit satellite according to an embodiment;

FIG. 13 is a histogram of Doppler offset within the field of view for a2 km by 2 km grid of locations according to an embodiment;

FIG. 14 is a schematic diagram of the division of the field of view intopositive and negative Doppler offset according to an embodiment;

FIG. 15 is a schematic diagram of grid based allocation exploitingDoppler to reuse slots more frequently according to an embodiment;

FIG. 16 is a plot of the result of optimising the transmit frequencydistribution for the given Doppler distribution of FIG. 13 according toan embodiment;

FIG. 17 is a plot showing the distribution of frequencies at thesatellite receiver for the cases where the transmitters all transmit atthe same centre frequency, and where the transmitter transmit using auniform transmit distribution and the optimised transmit frequencydistribution shown in FIG. 16 according to an embodiment;

FIG. 18 is a flow chart of a method for allocating a transmission slotto a terminal in a communication system according to an embodiment; and

FIG. 19 is a block diagram of a computing device according to anembodiment.

In the following description, like reference characters designate likeor corresponding parts throughout the figures.

DESCRIPTION OF EMBODIMENTS

Embodiments of a wireless communication system, such as that illustratedin FIG. 1, will be described in which terminals allocate or select atransmission slot based upon the geographic position of the terminal.That is the geographic position information, which is available to aterminal either from a memory, position determination module, or anotherdevice, is used to select a slot. FIG. 18 is a flow chart of a method180 for allocating a transmission slot to a terminal in a communicationsystem according to an embodiment. The method comprises the steps ofobtaining the current geographic position of the terminal 181; andallocating a transmission slot based upon the obtained geographicposition of the terminal 182. Multiple transmission slots may beallocated (ie one or more). The receiver may be a multiple access ormultiuser receiver that can successfully decode m≧1 simultaneoustransmissions within a single slot. It is to be noted that the methodscan be used in the case where the receiver can only decode a singletransmission in a slot (ie m=1). In this case the methods described canbe used to help distribute transmissions to avoid overlap. Embodimentsdescribed herein are also useful in communication systems where there isno feedback channel from the receiver to the terminals. In this caseallocation of a transmission slot is performed based on geographicposition, and independently of the receiver or other terminals. Howeverit is to be understood that embodiments of the methods described hereincan also be used where a feedback channel is present but is either notbeing used, or is being used for some other purpose. Similarlyembodiments of the methods described herein can also be used to assistin slot allocation in the case where a feedback channel is being used tocoordinate transmissions from several terminals.

The geographic position information may be obtained from a variety ofsources. For example, they may be placed in fixed locations and havetheir position programmed into a memory. Alternatively, they may have aglobal positioning system (GPS) receiver which provides an accurateposition and time reference. This is of particular importance in sensordeployments, where the sensors may wish to tag their measurements withthe geographic location and time of where and when the measurement wastaken. Other mechanisms whereby a terminal may obtain positioninformation include using location based services provided by a wirelesscommunications system. The terminal may receive the position over awireless link and pass the received position to the slot allocator. Inthis case, or in cases where the position is estimated or determinedfrom received signals (eg GPS) the position may only be temporarilystored, or stored in a transitory state (eg in a register or a buffer).The methods that we describe do not rely on the particular method bywhich geographic position of the terminal is provided. Further theobtained position may be an estimate of approximation of the actualposition of the terminal. The required accuracy of the estimation willtypically depend upon the implementation details, such as field of viewof the receiver, the distribution of terminals and whether there is aminimum position spacing's of terminals, etc.

Further, by using geographical information it is possible to takeadvantage of spatial re-use to allocate m terminals to each slot withinone field of view, and re-use those same slots elsewhere in anon-overlapping field of view. For example if the field of view is 10°of longitude (or latitude), the slot could be allocated based about thelongitude (or latitude) mod 10, so that a terminals with longitudes (orlatitudes) of 1°, 11°, 21°, etc would be allocated slot 1, and aterminals with longitudes (or latitudes)of 2°, 12°, 22°, etc would beallocated slot 2 This provides advantages over the fixed allocationmethod discussed above and is of particular importance in cellular orsatellite systems which aim to provide national or even global coverage.

FIG. 4 shows a block diagram of a transmitter 10 according to anembodiment. The terminal 10 includes a transmitter 11, transmitantenna(s) 12, a slot selector 13, and a memory or storage for storingthe current position of the terminal 14. The terminal also optionallyincludes a slot plan database 15 and optionally includes a positiondetermination function/module 16 and associated position determinationinput 17, such as an antenna. The transmitter, which is used tocommunicate data to the receiver, transmits its data in the slot, orslots identified by the slot selector. The details of the transmitter,e.g. specific modulator, data framing etc. are not shown, as our methodscan be used with a wide variety of different transmitters, as will beapparent to anyone skilled in the art. As described above, the slots maybe time slots, frequency slots, subcarriers, spreading sequences or anyhybrid combination of these, including variations using multipleantennas. In one embodiment the transmitter receives a binary datastream, or sequence, packet, or frame and performs transmission relatedfunctions such digital-to-analog conversion, filtering and modulationonto the selected carrier using an appropriate a modulation scheme (PSK,QAM, GMSK, OFDM etc). The transmitter may also implement functionalitysuch as error control coding, interleaving, insertion of pilot data etcto assist in increasing the robustness of the transmission to channeleffects, interference, and other noise sources. In one embodiment thetransmitter is used to send relatively short transmissions occupyingrelatively narrow bandwidth (eg 1, 2, 5, 10, 20, 40 kHz etc) in the VHFor UHF band.

The slot selector 13 takes as input the current position of the terminal14 and outputs one or more slot identifier(s), which are used by thetransmitter to select the slot for transmission. The specific format orcoding of the current position and slot identifier is immaterial to theinvention, and there are many ways that these may be represented aswould be apparent to the person skilled in the art (eg an integer in aslot sequence). The slot selector chooses slots according to somedeterministic or non-deterministic function of the current position, andoptionally the slot plan database. One example of a non-deterministicfunction is a random selection from a set of possible slots.

The current position of the terminal 14 is stored in a memory (eg RAM, aprocessor register, hard disk, flash memory etc) which contains thecurrent position (or position estimate) of the terminal. This may bepre-programmed, or it may be updated from time to time, either manually,or automatically, via an optional position determination device ormodule. The position may be stored as position according to a commongeographic coordinate system eg the position may be a latitude andlongitude according to WGS 84, or an (x,y) position in a localgeographic coordinate system. Alternatively the position could be gridreference or index in a common coordinate system used by thetransmitters and receivers.

The optional position determination module 16 provides position updatesto the current position store, based on signals that it receives fromits position determination input. The specific implementation of theposition determination function is immaterial to our method. It couldfor example be a global positioning system receiver, or alternatively,it could be a device which wirelessly accesses a network locationservice over a cellular or wireless local area network connection.

The optional slot plan database 15, described in more detail belowcontains a pre-programmed database which associates a geographic regionto one or more slot(s). That is the database stores mappings orrelationships R_(i)→{s_(j)} where R_(i) is the ith region, and {s_(j)}is the set of slots allocated to this region. The set of slots may be asingle slot or may contain up to p slots (ie j=1 . . . p). The number ofslots per region may be constant, and may be equal to the total numberof slots a receiver is able to simultaneously decode (i.e. p=m), or thenumber of slots per region may be varied. The database could be createdin a.variety of ways as would be known to the person skilled in the art.For example a mapping table could store region indexes and map these toslot indexes. Other tables may then map a region index to properties ofthe region, such as geographic boundaries. Similarly a slot database maymap a slot index to properties of the slot used for transmitting in theslot (eg timings, frequencies, spreading codes etc). This database maybe pre-programmed, or it may be updated from time to time, eithermanually or automatically via a wired or wireless connection (notshown). Allocating a transmission slot thus involves determining theregion linked to or containing the transmitters geographic positions,looking up or obtaining the set of slots associated with that region,and then selecting one of the slots from the set of slots.

The approach of using geographic position information available to theterminals in order to select slots has several advantages over prior artsolutions such as fixed allocation or random access, such as:

-   -   it does not require feedback from the receiver to the terminal;    -   it does not require communication between terminals;    -   it does not require real-time central coordination of slot        selection;    -   it supports terminal mobility and/or a moving field of view; and    -   it can greatly reduce (or even eliminate) the probability of        decoder failure at the receiver. This is accomplished for        example by using slot plans which use knowledge of the spatial        distribution of terminals (see the discussion on the slot plan        database).

The slot plan database 15 comprises of an association between geographicareas and slot(s). In one embodiment the slot plan database stores thisinformation hierarchically in a tree data structure in which each levelof the tree provides a finer grained division of the area. A memory inthe terminal can be used to store the database, and a processor cancontain software code or instructions to lookup entries in the database.Other hardware, software and combined hardware software implementationscan also be used.

Storing the database using a tree allows the slot selector to search thedatabase using well-known tree search methods, which allow the slotselector to reach a leaf of the tree in time that scales onlylogarithmically with the depth of the tree. Each leaf represents ageographic region, and has an associated set of slots. This has theadvantage that the slot selector can very rapidly determine the slot(s)from the current position. This tree is described in more detail below.

Various slot plans can be implemented with varying performance, and thechoice of the slot plan can be guided based upon expected implementationconditions. For example there is little point in assigning slots togeographic areas where there are known to be no terminals as this wastesavailable slots. Similarly assigning only a few slots to a largegeographic region which is expected to contain a large number ofterminals (for example many more than m terminals), will likely resultin a high failure probability. Thus in one embodiment knowledge of theexpected statistical spatial distribution of terminals (but notnecessarily the specific location of individual terminals, which may notbe known) is used in developing an efficient slot plan. For example theboundaries or size of each region in the database can be determinedbased upon expected statistical spatial distribution of terminals.However it is to be understood that a range of information about theexpected implementation may be used to develop an advantageous orefficient slot plan (assignment of slots to geographic areas)

Below we give three example embodiments of slot plan design which canimprove efficiency in certain implementations. In one embodiment eachslot is used only once within a field of view, regardless of theposition of the field of view, and slots may then be re-used innon-overlapping fields of views. In other embodiments a slot may be usedmore than once in a field of view (ie one or more times). In someembodiments a slot may be used at most a fixed number of times q in thefield of view. This fixed number may be based upon the characteristicsof the receiver. Typically q≦m, which m is the number of transmissionsthat the multiuser receiver is able to decode in a slot. Other slotplans can be designed by applying existing methods for frequencyplanning in cellular systems, or for spot-beam design in geostationarycommunications satellites.

Note that our approach is novel compared to these previous systems, asit uses geographic position information available to the terminal toautonomously decide which slot(s) to use. In a cellular system, thechannels are assigned by a central controller. In a spot beam satellitesystem, the available channels are determined by the design of thesatellite antenna, and are again centrally controlled. Embodiments ofthe system described herein do not require any central coordination.

In a first example embodiment, slot allocation is performed based upon arectangular grid. This can be used if the terminals are expected to beapproximately uniformly distributed throughout the total coverage area;which we will refer to as the plane. Suppose that the field of view canbe approximated by a rectangle 50, X meters by Y meters (we adoptCartesian coordinates for this example, however other coordinate systemscould be used). FIG. 5 shows a slot allocation method 50 based on arectangular grid. The horizontal direction 55 is divided into N columns,while the vertical direction 54 is divided into M rows. The field ofview is divided into NM non-overlapping rectangular regions 53 withhorizontal side 51 of length Δx and vertical side 52 of length Δy, andthus having an area of ΔxΔy square meters. To each of the NM regions 53,we can allocate one or more of the n slots. For example, if NM=n, theslot assigned to a region could be identified simply by the regionnumber 0, 1, 2, . . . , NM−1, or by any other one-to-one mapping. Thatis the region index=slot index, and each slot is only associated withone region. Alternatively, we could have more than one slot allocated toa region if NM<n. If the multiuser receiver can correctly decode mterminals in one slot, we can allocate each slot to at most m regions.

FIG. 6 shows a schematic diagram 60 of a tiling of the plane 61 bycopies of this rectangular grid 50 pattern. This tiling has the verybeneficial property that any X by Y meter rectangle placed on the planecontains exactly the same regions as the original grid pattern shown inFIG. 5, just re-arranged. Consider the X×Y field of view indicated bythe heavy outlined rectangle 62. This overlaps four of the tiledrectangles. However, as indicated by the labelling A, B, C, D, we seethat the field of view contains all of the same regions as the originalgrid, just re-arranged. This is the case no matter where the field ofview is placed on the plane.

For this tiling of grid assignments, the slot selector can determinewhich region it belongs to using modulo arithmetic. Suppose the terminalis at position (x, y) in the same coordinate system used by the grid andtiling. Then the region number R is determined by

R=N(y mod Y)+x mod X)   Equation 5

where a mod b is the well-known modulo operator, which computes theremainder after dividing a by b. Once the terminal knows which region itbelongs to, it can select its slot according to the assignments of slotsto regions. If only one slot has been assigned to region R, the slotselector chooses that slot. Alternatively, if region R has been assignedmore than one slot, it can choose from this list of slots randomly.

For the sake of comparison with the random access method describedabove, suppose now that NM=n/m and that each region has been assigned asingle slot, with each slot being assigned m times. In the case that theterminals are spatially distributed according to a two-dimensionalPoisson process with mean k/n, the performance of this scheme isidentical to the random access method described above.

However, in practice, terminals may be spatially distributed accordingto some other method. For example, they may be manually placed, orotherwise uniformly distributed on the plane such that there are only mterminals in each region.

In another scenario, the terminals may be randomly located, but adhereto some minimum separation distance d. This could be the case forvehicles, vessels or aircraft maintaining safe separation distances. Inthis scenario, if

$\begin{matrix}{{2\pi \; r^{2}} > {\frac{1}{m}\left( {{\Delta \; x} + r} \right)\left( {{\Delta \; y} + r} \right)}} & {{Equation}\mspace{14mu} 6}\end{matrix}$

there can never be more than m terminals within one region.

In such scenarios, this grid based assignment eliminates the probabilitythat too many terminals transmit using the same slot within the field ofview, no matter where the field of view is placed on the plane. Thistiling of grid assignments demonstrates that it is possible to devise aslot plan which has the property that no matter where the field of viewis placed, each slot is used only m times within the field of view. Thisallows us to eliminate the probability that the multiuser decoder cannotdecode due to too many terminals decoding in the same slot. Thisprovides a significant benefit compared to the random access methoddescribed above.

In a second example embodiment, slot allocation is performed based uponthe use of irregular partitions. The grid-based slot allocationdescribed above provides blanket coverage of the plane. This assumes auniform density of terminals over the plane. In practice, it may beknown that terminals follow some non-uniform density. For example, theremay be more terminals in urban areas than rural areas (or vice versa).In a maritime application, there may be more terminals in shipping lanesthan in other areas of the oceans (and no terminals on land areas).Similarly, in an aviation example, there may be more terminalsdistributed along heavily travelled flight paths. In such instances, itis beneficial to adopt an irregular partition of the plane. Anillustrative example is shown in FIG. 7 which is a schematic diagram ofthe irregular partitioning of an operational region (using an irregulargrid slot allocation scheme) according to an embodiment. The operationalregion may be region traced or swept out by a satellite rotating aroundthe earth, or an airborne receiver. The operation region may also be aportion of the total area swept out corresponding to a region (orregions) where terminals may use the system. This may exclude countrieswhere the system is not used. An irregular pattern allows the system toallocate more slots to areas where there are expected to be moreterminals Unlike the regular grid pattern and tiling discussed above,more care must be taken with irregular assignments to make sure thatregardless of the location of the field of view, that each slot appearsno more than m times within the field of view. One method to achievethis goal is to assign slots to regions using graph colouring, whichwill now be described. However it is to be noted that graph colouringcan also be used in the case of the region boundaries being regular (ega rectangular grid such as that shown in FIGS. 5 and 6).

Suppose that the dividing of the entire plane into regions has alreadybeen performed, and that the diameter of the field of view is D meters(if the field of view is not circular, D is the diameter of the smallestcircle that completely covers the field of view). Define a graph G=(V,E) with vertexes V and edges E as follows. For each region we create asingle vertex in the graph corresponding to that region. We create anedge between any pair of vertexes which correspond to regions that areseparated by less than D meters. We now apply known graph colouringalgorithms to assign one of the integers 1, 2, . . . , n to each vertex(these are the n “colours” in the graph colouring). This is alwayspossible if the chromatic number of the graph G is greater than n. Wecan now assign slots to regions according to the integers assigned tothe corresponding vertexes by the graph colouring algorithm. Using thissame graph G, we can even optimise the number of slots required by firstdetermining (or upper bounding) the chromatic number κ of the graph Gand setting n=κ. A graph colouring has the property that no two adjacentvertexes in the graph (vertexes joined by an edge) share the samecolour. Translating this to the slot allocation, this means that no tworegions closer than D meters will share the same slot. Since we havechosen D to be the diameter of the field of view, this yields thedesired property that regardless of where we place the field of view,each slot is used only once within the field of view. More generally wecan define the use of a bounding region rather than a minimum positionseparation. That is an edge is created between any pair of vertexes inthe graph which are within a bounding region. This can be a circle witha diameter D, for example where the circle is the smallest circle thatcompletely bounds the estimated field of view of the common receiver.However the bounding region could be a rectangle (eg sides X and Y), anellipse, a regular shape (hexagon, octagon), or even an irregular shape.These shapes may be shaped which cover an expected field of view, or aswill be discussed below in relation to Doppler induced frequency reuse,half of the expected field of view. For example the bounding regioncould be a rectangular region with sides X and Y, where X=2Y and the Ydimension is aligned with the direction of motion of the receiver.

As mentioned earlier, it is convenient to store the slot plan databaseusing a tree data structure. The tree consists of nodes and branches.One node is identified as the root node. The depth of a node is thenumber of branches between it and the root. The root is depth zero.Child branches connect parent nodes at depth d to child nodes at depthd+1. FIG. 8 is a schematic diagram 80 of an irregular partition of anarea according to an embodiment and FIG. 9 is a schematic diagram 90 ofa slot plan database stored as a tree according to an embodiment. Webegin by supposing that we have a given partition of the plane intoregions, and a given assignment of slots to regions.

Each level of the tree successively divides the plane into smaller andsmaller areas. Each node in the tree is labelled with a pair (x_(i),y_(i)), where i=0, 1, 2, . . . is a dummy index which ranges from zeroup to the total number of nodes in the tree minus one. Each leaf thetree (a leaf is a node with child branches) corresponds to a region ofthe slot plan is labelled with a set of slots. Each non-leaf node hasfour children. Each of these corresponds to the four possibilities ofcomparing an arbitrary point (x, y) to its node label (x_(i), y_(i)). Welabel these branches as follows: (<, <) means the area where x<x_(i),and y<y_(i); (≧, <) means the area x≧x_(i) and y<y_(i); (<, ≧) means thearea x<x_(i), and y≧y_(i) and finally (≧, ≧) means the area x≧x_(i) andy≧y_(i). Note that we could also use ≦and> in place of <and≧.

The slot selector operates as follows. Given the current position (x, y)it compares this position to the (x₀, y₀) associated with the root node.It follows the branch corresponding to the relation between (x, y) and(x₀, y₀), arriving at node, which for clarity we will suppose has theindex 1. It now compares (x, y) to (x₁, y₁), and takes the correspondingbranch. This process is repeated, at each depth of the tree, followingthe branch corresponding to the outcome of comparing (x, y) with thenode label. Upon reaching a leaf, the process terminates, and the slotselector outputs the set of slot identifiers associated with that leaf.FIG. 9 shows an example of this process, depicting the traversal of thetree (only the relevant parts of the tree are shown) that takes placefor a terminal located anywhere within the shaded region on FIG. 8. Forexample we have x≧x₀ and y≧y₀ and thus branch 91 is selected in FIG. 9.With reference to FIG. 8, the location is narrowed to the region boundedby lines 81 (x₀) and 82 (y₀). In the next comparison we have x<x₁ andy<y₁, and thus branch 92 is selected, and in FIG. 8, the location isnarrowed to the region bounded by lines 81 and 82, and 83 (x₁) and 84(y₁). In the next comparison we have x≧x₂ and y≧y₂ and thus branch 93 isselected in FIG. 9. With reference to FIG. 8, the location is narrowedto the region bounded by lines 85 (x₂) and 86 (y₂), and 83 (x₁) and 84(y₁). In the next comparison we have x≧x₃ and y<y₃ and thus branch 94 isselected in FIG. 9. With reference to FIG. 8, the location is narrowedto the region bounded by lines 87 (x₃) and 86 (y₂), and 83 (x₁) and 88(y₃). The terminal is thus at a leaf 95 of the tree and the terminal islocated in geographic region 89, and an appropriate slot can be selectedfrom slots {a, b, c, , , , } allocated to this geographic region).

Note that not every leaf in the tree has to be at the same depth. Thisallows for irregular partitions of the plane. Also note that the (x_(i),y_(i)), i=0, 1, 2, . . . labelling the nodes do not have to fall on anyregular grid. Finally, this whole setup can be extended to a trelliswhere there can be multiple paths from the root node to any leaf, orsimilar structures (eg directed acyclic graph). This allows for a morecompact representation when multiple regions share the same slotallocation. More sophisticated slot plans (e.g. non-rectangular regions)can also be represented on a tree or trellis, by appropriately modifyingthe node labels and decision function for traversing the tree.

In another embodiment a hybrid approach may be used in which localcoordination is performed by standard or traditional slot allocationmethods with global coordination by geographic allocation. In somesystems, different groups of terminals may be equipped with a method oflocally coordinating their choice of slot within their group. Forexample, they might access the channel using carrier sense multipleaccess with collision avoidance. Another example of local coordinationis self-organising time division multiple access (SOTDMA). Their localcoordination may even be controlled by some centralised controller, e.g.a base station or access point. However different groups of terminalsmay have no way to globally coordinate their choice of slot, lackingdirect communication between groups (for example the groups are locatedfar away from each other and have no direct connection).

FIG. 10 is a schematic diagram of a communications system 1 using oflocal coordination of transmitters according to an embodiment.Transmitters 10 in the field of view 3 of a satellite receiver aregrouped into a first local group 101 and a second local group 102. Eachof the local groups can locally coordinate their slot selection, howevereach group is unaware of the other group and its choice of slots. Such ascenario could arise for example in a low earth orbit system where theterminals form a local ad hoc wireless network, however the local groupscould be separated by thousands of kilometres and be unaware of eachother's existence. The satellite receiver 2 wishes to receive data fromall of the terminals. In such scenarios, we can adapt our approach toassign groups of slots to distinct geographic regions (using any of themethods described above). The terminals then perform their own localcoordination (using whatever method they choose, such as under thedirection of a local controller) within the group, using the group ofslots allocated to their region.

FIG. 11 is a block diagram of a terminal 10 with local slot coordinationaccording to an embodiment. The transmitter is similar to that shown inFIG. 4, and further includes a local slot selector 18. In thisembodiment the slot selector 13 selects a set of slots based upon thecurrent geographic position, and this set of slots is provided to thelocal slot selector 18, which operates according to whatever localcoordination method is in in use. The local slot selector 18 takes asinput a set of slots from the slot selector 13, and then chooses a slotfrom within this set. The local slot selector may use local slotcoordination input 19, such as an antenna, to assist in choosing theslot. In one embodiment, the antenna may be connected through asubsystem that will provide the input. In one embodiment the subsystemmay include a receiver that can detect the presence of other nearbytransmitters, e.g. as part of a transceiver performing SOTDMA. In oneembodiment the local slot coordination input 19 is connected to anotherdevice which may indicate the presence of other local terminals, orprovide information or instructions for local slot coordination eg howmany terminals, what method to use, or even which slot to choose fromthe set of slots.

In the example shown in FIG. 10, the first local group 101 could beassigned slots 1 to 10 based upon its geographic position (for examplebased upon the centre of the field of view), and the second local group102 could be assigned slots 31 to 40. For example in one embodiment thefirst local group 101 could use random allocation using the set of slots1-10 provided by the slot selector, with the three transmitters randomlyselecting slots 2, 4 and 7. The second local group 102 could use a fixedallocation scheme within the group. For example each transmitter couldbe assigned an index i, and the local slot selector would selecting theith slot in the set of assigned slots. Thus in this case the threetransmitters would be assigned slots 31, 32 and 33 from slots 31-40. Inanother example, the second local group 102 could perform SOTDMA witheach terminal electing to transmit only in slots from the set ofassigned slots. The local slot selector 18 could be made aware of thepresence of other terminals via the local slot coordination input 19from a receiver that can detect the presence of other nearbytransmitters.

The large orbital velocity of a low earth orbit satellite inducessignificant Doppler offsets in signals transmitted to or from thesatellite. FIG. 12 shows a plot of the Doppler offset experienced byterminals located within the field of view of a low earth orbitsatellite for a signal transmitted in the VHF band. This offset variesbetween approximately −3600 Hz up to +3600 Hz and dashed lines indicateoffset contours of −1000 Hz, −2000 Hz and −3000 Hz, and dotted linesindicate contours of +1000, +2000 and +3000 Hz. The satellite nadir isat (0, 0) and the figure is oriented so that the satellite track isalong the vertical axis, moving from top to bottom.

FIG. 13 is a plot of the corresponding histogram of Doppler offsets fromFIG. 12, where we have considered every location on a 2 km by 2 km gridwithin the field of view. From this histogram, we can see that thedistribution of Doppler offset is heavily skewed toward the positive andnegative extremes. In an open-loop scenario, where ground basedterminals have no way of receiving a signal from the satellite, andadditionally do not have any knowledge of the satellite orbits, theterminals do not know ahead of time the Doppler offset that will affectthe signals that they transmit to the satellite. As a result, suchterminals cannot pre-compensate for the Doppler shift. This unknownDoppler shift can potentially make it difficult to use frequencyslotting (channelization) in the schemes described above. However,several novel methods have been developed to exploit the frequencydiversity that this Doppler shift offers, and will now be discussed.

The first example embodiment is Doppler-induced Frequency Reuse. First,consider a system where the terminals are not free to choose thetransmit frequency (for example, due to regulatory constraints). In sucha system it is possible to use some other kind of slotting, for exampletime slotting, and use the unknown Doppler offset to permit tighterspatial reuse of slots. FIG. 14 shows a schematic diagram 140 of thedivision of the field of view 141 into negative Doppler offsets 143(trailing the satellite) and positive Doppler offsets 144 (leading thesatellite) for a satellite travelling from north to south 142. We candivide the plane into alternating horizontal bands of R meters andadopting one of the geographic based slot plans described above, wherethe field of view is now redefined to be a rectangle 2R metershorizontally by R meters vertically (instead of 2R×2R). This iseffectively doubles the number of slots available for allocation. FIG.15 is a schematic diagram 150 of grid based allocation exploitingDoppler to reuse slots more frequently according to an embodiment. Thesame idea applies to the other allocation methods described above. Wesee that just like FIG. 6, we have tiled the plane, where now the fieldof view 141 is 2R×R (outer bounding the circular satellite field of viewby a rectangle). We see that each portion of the slot allocation nowappears at most twice within the circular footprint of the satellite.However, each portion appears once with a positive Doppler offset andonce with a negative Doppler offset. If the signal bandwidth isrelatively narrow compared to the maximum Doppler offset, e.g. 1 kHz forthe example of FIG. 12, the positive and negative versions on each slotwill be separated in frequency by the Doppler shift. With reference toFIG. 13, the absolute Doppler shift is most likely near the maximum,providing maximal frequency separation. More generally the step ofassigning a set of one or more slots to each geographic region could beperformed using Doppler induced frequency reuse. In this case the sameset of slots are used (or re-used) for both a first geographic regionand a second geographic region. These correspond to different regions ina common field of view of the common receiver with the first regionhaving positive Doppler offsets and the second region having negativeDoppler offsets.

The second example embodiment is Optimised Probabilistic FrequencyDivision Multiple Access. FIG. 13 shows that the Doppler offsetexperienced by a terminal is much more likely to be near the maximum orminimum than somewhere in between. In the method described above, thisresults in a higher proportion of signals received at maximum or minimumDoppler offset. Suppose that we wish to use (for example) time-frequencyslots, defined not only by a particular time duration, but also by afrequency channel. This falls completely within the general concept of aslot described earlier, and all of the methods described so far apply.While we get a substantial benefit (a factor of two) from the Dopplerinduced frequency reuse, we would get even more benefit if it werepossible to arrange the transmissions such that the signals were moreuniformly distributed over the frequency band. In the scenario whereterminals can control their transmit frequency to some degree, we havedeveloped a novel and powerful method to ensure that the signalsreceived at the satellite are indeed uniformly distributed over thefrequency band. The key observation is to determine a distribution oftransmission frequencies for the terminals such that, after the effectof Doppler, the satellite sees a uniform distribution. This can beformulated as a problem in numerical optimisation as follows. Let theterminals have a transmission frequency distribution described by theprobability density function q(f). Let the distribution of Dopplershifts be described by the probability distribution d(f). Then thedistribution of frequency at the satellite is d*f, where * is the linearconvolution operator. This is due to the fact that the Doppler shift isadditive and that the distribution of the addition of two randomvariables is well known to be given by their convolution.

We can now solve a numerical optimisation problem to find the optimal q*as follows:

$\begin{matrix}{q^{*} = {\arg \; {\min\limits_{q}{{J\left( {d*q} \right)}\mspace{14mu} {subject}\mspace{14mu} {to}}}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$∫q(f)df=1   Equation 8

q(f)≧0   Equation 9

where J(•) is a functional that can be chosen by the designer as anyreal valued objective function which is small when its argument is“close” to uniform, and large when it is “far away” from uniform. Thetwo constraints on q(f) are to ensure that it is a valid probabilitydensity function. This procedure can also be applied to the case that qand/or d are discrete, i.e. are probability mass functions. In thatcase, the constraints on q(f) become

$\begin{matrix}{{\sum\limits_{f_{i}}{q\left( f_{i} \right)}} = 1} & {{Equation}\mspace{14mu} 10}\end{matrix}$q(f _(i))≧0   Equation 11

where the f_(i) are a set of discrete frequencies chosen by thedesigner. Several choices are possible for J. One example is

$\begin{matrix}{{J\left( {p(f)} \right)} = {{\alpha - p}}_{2}^{2}} & {{Equation}\mspace{14mu} 12} \\{\mspace{85mu} {= {\int{\left\lbrack {{p(f)} - \alpha^{2}} \right\rbrack^{2}{f}}}}} & {{Equation}\mspace{14mu} 13}\end{matrix}$

where α is the uniform distribution over the support of p. For exampleif p(f) has support (the range of frequencies over which p(f)>0) equalto W Hz, then α=1/W. This choice of J aims to minimise the least squaresdifference between p=q*d and the uniform distribution. Another approachwould be to set J(p)=−H(p) to be the negative of the Shannon entropy ofp. For a discrete distribution p, the entropy is maximised for theuniform distribution. Other objective functionals are possible, and ourmethod applies to all of them. Standard numerical optimisation packagescan be used to implement the required constrained minimisation. Forexample, the least squares approach can be solved in MATLAB using thefunction 1slin. In Mathematica, the function FindMinimum can be used,even for non-linear objective functions.

FIG. 16 is a plot 161 of the result of optimising the transmit frequencydistribution for the given Doppler distribution of FIG. 13 according toan embodiment. For this example, the Shannon entropy was taken as theobjective functional. Using the least mean squares approach yields asimilar (but different) result.

FIG. 17 is a plot of the distribution of frequencies at the satellitereceiver for several transmit frequency distributions—the un-optimiseddistribution 171, the uniform transmit distribution 172 and theoptimised transmit distribution 173. Each curve is the resultingdistribution at the receiver after passing through the channel andincludes the combined effect of the applied transmit offset and channelDoppler effect. In each case the transmitters all transmit at the samecentre frequency and the centre frequency has been subtracted to centrethe graph at 0 Hz. The un-optimised distribution 171 is shown forreference and in this case no frequency offsets are applied at thetransmitters and the resultant distribution at the receiver illustratesthe channel induced frequency offsets due to Doppler effects (ie nooptimisation case). The uniform transmit distribution 172 illustrates isthe resulting distribution at the receiver where the transmitters applya frequency offset selected from a uniform distribution. That is theprobability density function q* for the transmission frequencies used bythe terminals is uniform. The optimised transmit frequency distribution173 illustrates is the resulting distribution at the receiver where thetransmitters apply a frequency offset from an optimised distribution. Inthis case the optimised distribution is obtained by optimising thetransmit frequency distribution for the given Doppler distribution ofFIG. 13 as outlined above. Using the optimised transmit frequencydistribution 173 gets the received spectrum closer (in fact as close aspossible) to a uniform distribution at the receiver. We can see that notonly do we improve the shape of the received distribution, we have alsoincreased the overall bandwidth (doubled in this example—compare theoptimised distribution 173 with the un-optimised distribution 171). Thishas the additional benefit of increasing the number of slots availablefor use. Once an optimal transmit frequency distribution q* is obtained,it can be applied in several ways. First, each terminal could choose arandom frequency offset according to the distribution q*. With manyterminals uniformly distributed over the field of view, the satellitewill see the optimised distribution d*q*. Alternatively, we can assignfrequencies deterministically to terminals by associating frequencies toslots in a geographic slot plan (using any of the methods describedearlier), where we ensure that the proportion of each frequency used inthe slot plan is according to q*. We also observe that applying theuniform transmit frequency distribution 172 results in a receivedspectrum that is much closer to the uniform distribution than theun-optimised distribution 171, but avoids the effort of calculating anoptimised distribution. We may also design the transmission frequencydistribution such that it is limited within a certain (ie predefined)bandwidth, at the transmitter and/or at the receiver (taking intoaccount the expected Doppler distribution). For example the predefinedbandwidth may be defined in order to meet system or regulatoryconstraints (in which case its value can be determined during systemdesign or configuration).

Embodiments of the methods and transmitters may be implemented in arange of wireless communication systems using a wide range ofcommunication technologies. This may include wireless communicationsystems, and transmitters and receivers described in AustralianProvisional Patent Application No. 2012904130 titled “Communicationsystem and method” filed on 21 Sep. 2012; and Australian ProvisionalPatent Application No. 2012904145 entitled “Multiaccess CommunicationSystem” filed on 21 Sep. 2012. The content of each of these applicationsis hereby incorporated by reference in their entirety. Embodiments canbe used in communication systems for supporting widely distributedsensor and devices, such as terrestrial and maritime field sensors andindustrial automation and control equipment. The capability to supportsuch devices and sensors has the potential to deliver significanteconomic and environmental benefits in areas such as environmentalmonitoring for climate change, water, mining, agriculture, Defence andNational security. For example potential applications include supportingcommunications with long range oceanic environmental monitoring forenvironmental, economic and national security reasons or remotemonitoring of unattended ground sensors or assets. For such sensorssatellite or airborne communications is the only feasible solution forextraction of data from these sensor and assets. Embodiments of themethods described herein enable efficient slot allocation to supportlarge numbers of distributed terminals.

Various methods and systems have been described herein which providesolutions for determining how to allocate terminals to slots in order tomaximise (or improve) communication system performance, particularly inthe case where there is no feedback channel between a receiver (such asa satellite receiver) and terminals within the field of view (orreceiver area) of the receiver. However it is to be understood that themethods described herein can also be applied in communication systemswhere a feedback channel is present but is either not being used, or isbeing used for some other purpose. Similarly embodiments of the methodsdescribed herein can also be used to assist in slot allocation in thecase where a feedback channel is being used to coordinate transmissionsfrom several terminals. The approach taken is to use geographic positioninformation available to the terminals on their geographic position inorder to select a slot for a terminal to use to communicate (ie sendtransmissions) to the receiver. Terminals can be programmed with a slotselector to choose slots according to some deterministic ornon-deterministic function of the current position. A slot plan databasemay be used to assist in efficient slot selection. The approach hasseveral advantages. There is no requirement for feedback from theterminal to the receiver, or for communication between terminals. Alsoit does not require real-time central coordination of slot selection,and supports terminal mobility and/or a moving field of view (ie movingsatellite, or long range unmanned aerial vehicle (UAV)). The approachcan also greatly reduce or eliminate the probability of failure at thereceiver. This has numerous implementation advantages such as reducedcost, complexity, and power consumption. The methods can be used in thecase where the receiver is a multiple access or multiuser receiver thatcan successfully decode m≧1 simultaneous transmissions within a singleslot. It is to be noted that the methods can still be used in the casewhere the receiver can only decode a single transmission in a slot (iem=1). In, this case the methods described can be used to help distributetransmissions to avoid overlap.

The slot plan used by the slot plan database may allocate each slot oncewithin the field of view. Use of the geographic position, allows theterminally to autonomously decide which slot to use. The slot plan maybe based upon tiling regions within a rectangular grid. In suchscenarios, this grid based assignment eliminates the probability thattoo many terminals transmit using the same slot within the field ofview, no matter where the field of view is placed on the plane. Thistiling of grid assignments demonstrates that it is possible to devise aslot plan which has the property that no matter where the field of viewis placed, each slot is used only m times within the field of view. Thisallows us to eliminate the probability that the multiuser decoder cannotdecode due to too many terminals decoding in the same slot. Thisprovides a significant benefit compared to the random access methoddescribed above.

The plan may use an irregular grid and allocation using graph colouring.Further slots geographic regions may be defined within the field ofview, with each region assigned a group of slots. Allocation of slotsfrom the assigned group may be locally coordinated within the group. Theslot plan database may be stored as a tree or trellis structure whichcan be efficiently searched. In a further aspect the field of view maybe divided into positive and negative Doppler regions and slots may bereused in the two regions to double the number of slots available forallocation. Further benefit may be obtained by allocation of slots sothat the receiver sees an approximately uniform distribution offrequencies over the frequency band. This may be further based uponobtaining a probability density function q* for the transmissionfrequencies used by the terminals. This may be obtained based uponnumerical optimisation techniques.

The methods described herein may be a computer implemented using one ormore computing devices. The computing device may comprise a processorand a memory, and one or more input or output devices. The memory maycomprise instructions to cause the processor to execute a methoddescribed herein. These instructions may be stored as computer codes,which are loaded and executed. The computing device may be a standardcomputing device, such as a desktop computer or laptop, a server or aportable computing device or board for inclusion in another apparatus orsystem. The computing device may be an embedded system in an apparatus.The computing device may be a unitary computing or programmable device,or a distributed device comprising several components operatively (orfunctionally) connected via wired or wireless connections. An embodimentof a computing device 190 is illustrated in FIG. 19 and comprises acentral processing unit (CPU) 191, a memory 195, an optionally a displayapparatus 196 and an input device 197 such as keyboard, mouse, etc. TheCPU 191 comprises an Input/Output Interface 192, an Arithmetic and LogicUnit (ALU) 193 and a Control Unit and Program Counter element 194 whichis in communication with input and output devices through theInput/Output Interface. The Input/Output Interface may comprise anetwork interface and/or communications module for communicating with anequivalent communications module in another device using a predefinedcommunications protocol (e.g. Bluetooth, Zigbee, IEEE 802.15, IEEE802.11, TCP/IP, UDP, etc). A graphical processing unit (GPU) may also beincluded. The display apparatus may comprise a flat screen display (egLCD, LED, plasma, touch screen, etc), a projector, CRT, etc. Thecomputing device may comprise a single CPU (core) or multiple CPU's(multiple core). The computing device may use a parallel processor, avector processor, or be a distributed computing device. The memory isoperatively coupled to the processor(s) and may comprise RAM and ROMcomponents, and may be provided within or external to the device. Thememory may be used to store the operating system and additional softwaremodules that can be loaded and executed by the processor(s).

Those of skill in the art would understand that information and signalsmay be represented using any of a variety of technologies andtechniques. For example, data, instructions, commands, information,signals, bits, symbols, and chips may be referenced throughout the abovedescription may be represented by voltages, currents, electromagneticwaves, magnetic fields or particles, optical fields or particles, or anycombination thereof.

Those of skill in the art would further appreciate that the variousillustrative logical blocks, modules, circuits, and algorithm stepsdescribed in connection with the embodiments disclosed herein may beimplemented as electronic hardware, computer software, or combinationsof both. To clearly illustrate this interchangeability of hardware andsoftware, various illustrative components, blocks, modules, circuits,and steps have been described above generally in terms of theirfunctionality. Whether such functionality is implemented as hardware orsoftware depends upon the particular application and design constraintsimposed on the overall system. Skilled artisans may implement thedescribed functionality in varying ways for each particular application,but such implementation decisions should not be interpreted as causing adeparture from the scope of the present invention.

The steps of a method or algorithm described in connection with theembodiments disclosed herein may be embodied directly in hardware, in asoftware module executed by a processor, or in a combination of the two.For a hardware implementation, processing may be implemented within oneor more application specific integrated circuits (ASICs), digital signalprocessors (DSPs), digital signal processing devices (DSPDs),programmable logic devices (PLDs), field programmable gate arrays(FPGAs), processors, controllers, micro-controllers, microprocessors,other electronic units designed to perform the functions describedherein, or a combination thereof. A central processing unit (CPU) may beused, containing an Input/Output Interface, an Arithmetic and Logic Unit(ALU) and a Control Unit and Program Counter element which is incommunication with input and output devices or modules through theInput/Output Interface, and a memory. Software modules, also known ascomputer programs, computer codes, or instructions, may contain a numbera number of source code or object code segments or instructions, and mayreside in any computer readable medium such as a RAM memory, flashmemory, ROM memory, EPROM memory, registers, hard disk, a removabledisk, a CD-ROM, a DVD-ROM or any other form of computer readable medium.In the alternative, the computer readable medium may be integral to theprocessor. The processor and the computer readable medium may reside inan ASIC or related device. The software codes may be stored in a memoryunit and executed by a processor. The memory unit may be implementedwithin the processor or external to the processor, in which case it canbe communicatively coupled to the processor via various means as isknown in the art.

Throughout the specification and the claims that follow, unless thecontext requires otherwise, the words “comprise” and “include” andvariations such as “comprising” and “including” will be understood toimply the inclusion of a stated integer or group of integers, but notthe exclusion of any other integer or group of integers.

The reference to any prior art in this specification is not, and shouldnot be taken as, an acknowledgement of any form of suggestion that suchprior art forms part of the common general knowledge.

It will be appreciated by those skilled in the art that the invention isnot restricted in its use to the particular application described.Neither is the present invention restricted in its preferred embodimentwith regard to the particular elements and/or features described ordepicted herein. It will be appreciated that the invention is notlimited to the embodiment or embodiments disclosed, but is capable ofnumerous rearrangements, modifications and substitutions withoutdeparting from the scope of the invention.

1. A method for allocating a transmission slot to a terminal in acommunication system, the method comprising: obtaining a geographicposition of the terminal, wherein the communication system comprising aplurality of terminals and a receiver for receiving transmissions fromthe plurality of terminals, the receiver having a field of view, whereinthe terminal is one of the plurality of terminals; and allocating atransmission slot based upon the obtained geographic position of theterminal, wherein there is no feedback channel from the receiver to theplurality of terminals or a feedback channel from the receiver to theplurality of terminals is present but is not being used for allocationof the transmission slot to the terminal and allocation of thetransmission slot is performed independently of the receiver. 2.(canceled)
 3. The method as claimed in claim 1, wherein the geographicposition of the terminal is obtained from a memory, a positiondetermination module, or over a communication link.
 4. (canceled) 5.(canceled)
 6. The method as claimed in claim 1, wherein each terminalincludes a slot plan database comprising a plurality of geographicregions, and each geographic region is associated with a set of one ormore slots, and allocating the transmission slot comprises the furthersteps of: determining the geographic region that contains the geographicposition of the terminal; and selecting a slot from the set of one ormore slots associated with the determined geographic region.
 7. Themethod as claimed in claim 6, wherein each of the geographic regions inthe slot plan database has a boundary, and each of the boundaries aredetermined based upon the statistical spatial distribution of terminals.8. (canceled)
 9. The method as claimed in claim 6, wherein each slot isassociated with at most m regions.
 10. The method as claimed in claim 6,wherein the plurality of geographic regions form an operating region andeach of the geographic regions in the slot plan database has a boundary,and the boundaries of the regions are irregular such that regions forman irregular partition of the operational region.
 11. The method asclaimed in claim 6, further comprising the step of assigning a set ofone or more slots to each geographic region using a graph colouringalgorithm, wherein each geographic region is associated with a singlevertex in a graph, and an edge is created between any pair of vertexesin the graph which are within a bounding region.
 12. (canceled) 13.(canceled)
 14. The method as claimed in claim 11, wherein the boundingregion is a smallest circle that completely bounds an estimated field ofview of the receiver.
 15. The method as claimed in claim 6, wherein eachof the geographic regions is a rectangle geographic region and the slotplan database stores geographic regions which form a rectangular grid,and the step of determining the geographic region that contains thegeographic position of the terminal comprises determining a geographicregion number.
 16. (canceled)
 17. (canceled)
 18. The method as claimedin claim 6, further comprising the step of assigning the set of one ormore slots to each geographic region wherein the same set of slots areused for both a first region and a second region, and the first andsecond regions correspond to different regions in a common field of viewof the receiver, the first region having positive Doppler offsets andthe second region having negative Doppler offsets.
 19. The method asclaimed in claim 6, wherein the set of one or more slots is a pluralityof slots, and the step of selecting a slot from the set of one or moreslots associated with the determined geographic region is performed bylocally coordinating selection of the slot from the set of slots withina local group of terminals.
 20. The method as claimed in claim 6, wherethe slot plan database is stored as either a tree data structure, or atrellis data structure.
 21. (canceled)
 22. The method as claimed inclaim 1, wherein the terminals can control their transmission frequency,and allocation of slots to the terminals is performed so that thereceiver sees an approximately uniform distribution of frequencies overthe frequency band.
 23. The method as claimed in claim 22, wherein aprobability density function q* for the transmission frequencies used bythe terminals is obtained, and each terminal randomly choses a frequencyoffset based upon the obtained probability density function q* for thetransmission frequencies used by the terminals.
 24. The method asclaimed in claim 23, wherein the probability density function q* for thetransmission frequencies used by the terminals is either uniform or isobtained by a numerical simulation, wherein transmission frequencies aredeterministically assigned to each terminal by associating transmissionfrequencies to slots in a geographic slot plan, and the proportion ofeach transmission frequency used in the geographic slot plan isaccording to q*.
 25. (canceled)
 26. (canceled)
 27. A terminal for use ina communication system comprising: a receiver; and a plurality ofterminals, wherein the terminal is one of the plurality of terminals,the terminal comprising: a transmitter; a position module which obtainsa geographic position of the terminal; and a slot selector module forselecting a transmission slot based upon the obtained geographicposition, wherein there is no feedback channel from the receiver to theterminal or a feedback channel from the receiver to the terminal ispresent but is not being used for allocation of the transmission slot tothe terminal and allocation of the transmission slot to the terminal isperformed independently of the receiver.
 28. The terminal as claimed inclaim 27, wherein the position module obtains the geographic positionfrom at least one of a memory; a position determination module forestimating the position of the terminal or a position receiver forreceiving a position over a communication link.
 29. (canceled) 30.(canceled)
 31. (canceled)
 32. The terminal as claimed in claim 27further comprising: a local slot selector module and a local slotcoordination input, wherein the slot selector module is furtherconfigured to provide a plurality of slots based upon the obtainedposition to the local slot selector module, and the local slot selectormodule is configured to select a slot from the plurality of slots basedusing local coordination with one or more transmitters using a localcoordination input received from local slot coordination input.
 33. Theterminal as claimed in claim 27, wherein the slot selector modulefurther comprises: a slot plan database which comprises a plurality ofgeographic regions, and each geographic region is associated with a setof one or more slots, and the slot selector module is configured todetermine the geographic region that contains the geographic position ofthe terminal and select a slot from the set of one or more slotsassociated with the determined geographic region.
 34. (canceled) 35.(canceled)
 36. (canceled)
 37. (canceled)
 38. (canceled)
 39. (canceled)40. (canceled)
 41. (canceled)
 42. (canceled)
 43. (canceled) 44.(canceled)
 45. (canceled)
 46. (canceled)
 47. (canceled)
 48. (canceled)49. (canceled)
 50. (canceled)
 51. (canceled)
 52. (canceled) 53.(canceled)
 54. A communication system, comprising: a plurality ofterminals; and a receiver for receiving transmissions from the pluralityof terminals, each terminal comprising: a transmitter; a position modulewhich obtains a position of the terminal; and a slot selector module forselecting a transmission slot based upon the obtained position of theterminal, wherein there is no feedback channel from the receiver to theplurality of terminals or a feedback channel from the receiver to theplurality of terminals is present but is not being used for allocationof a transmission slot to the terminal and allocation of a transmissionslot to the terminal is performed independently of the receiver.